The present invention relates to ion accelerators in general and to helical ion accelerators in particular. Accelerators of ions have many practical uses in addition to basic research which vary from ion implantation, such as used to form semiconductors or coatings, to neutron radiography used to detect explosives and nuclear materials in luggage and shipping containers. The development of the helical ion accelerator, also called a pulse line ion accelerator, was motivated by the desire for a less expensive way to accelerate intense short pulse heavy ion beams to regimes of interest for studies of high energy density physics and warm dense matter. In helical ion accelerators a pulse power driver applied at one end of a helical pulse line creates a traveling wave pulse that accelerates and axially confines a heavy ion beam pulse. Richard Briggs described acceleration scenarios with constant parameter helical lines which result in output energies of a single stage much larger than the several hundred kilovolt peak voltages on the line. The concept can be described as an “air core” coax line where a pulse is injected into a central helical core so that an accelerating voltage pulse moves along with the ions to get voltage multiplication.